|
%I #14 Apr 27 2020 02:26:52
%S 1,1,2,3,4,5,6,7,7,8,9,10,11,12,13,13,14,15,16,17,18,19,20,20,21,22,
%T 23,24,25,26,26,27,28,29,30,31,32,32,33,34,35,36,37,38,39,39,40,41,42,
%U 43,44,45,45,46,47,48,49,50,51,52,52,53,54,55,56,57,58,58
%N Floor of the expected number of occupied cells in a random placement of 2n balls into n cells.
%C Also floor of expected number of distinct symbols in sequences on n symbols of length 2n.
%F a(n) = floor(n*(1-(1-1/n)^(2*n))).
%e For n=2, with symbols 0 and 1, the 2^4 sequences on 2 symbols of length 4 can be represented by 0000, 0001, 0010, 0011, 0100, 0101, 0110, 0111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, and 1111. We have 2 sequences with a unique symbol, and 14 sequences with 2 symbols, so a(2) = floor((14*2+2)/16) = floor(15/8) = 1.
%t Table[Floor[n*(1 - (1 - 1/n)^(2 n))], {n, 100}] (* _T. D. Noe_, Mar 15 2012 *)
%Y Cf. A209899.
%K nonn
%O 1,3
%A _Washington Bomfim_, Mar 14 2012
|
